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On the detection of several obstacles in 2D Stokes flow: Topological sensitivity and combination with shape derivatives
On a transmission eigenvalue problem for a spherically stratified coated dielectric
1. | Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553, United States, United States |
References:
[1] |
T. Aktosun, D. Gintides and V. G. Papanicolaou, The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems, 27 (2011), 115004, 17pp.
doi: 10.1088/0266-5611/27/11/115004. |
[2] |
T. Aktosun and V. G. Papanicolaou, Reconstruction of the wave speed from transmission eigenvalues for spherically symmetric variable-speed wave equation, Inverse Problems, 29 (2013), 055007, 19pp.
doi: 10.1088/0266-5611/29/6/065007. |
[3] |
A. Baker, Transcendental Number Theory, Cambridge University Press, Cambridge, 1975. |
[4] |
F. Cakoni and D. Colton, A Qualitative Approach to Inverse Scattering Theory, Applied Mathematical Sciences Series Volume 188, Sringer, New York 2014.
doi: 10.1007/978-1-4614-8827-9. |
[5] |
F. Cakoni, D. Colton and D. Gintides, The interior transmission eigenvalue problem, SIAM J. Math Anal., 42 (2010), 2912-2921.
doi: 10.1137/100793542. |
[6] |
R. Courant and D. Hilbert, Methods of Mathematical Physics, Volume I, Interscience Publishing, New York, 1953. |
[7] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed., Applied Mathematical Sciences, 93. Springer, New York, 2013.
doi: 10.1007/978-1-4614-4942-3. |
[8] |
D. Colton and Y. J. Leung, Complex Eigenvalues and the inverse spectral problem for transmission eigenvalues, Inverse Problems, 29 (2013), 104008, 6pp.
doi: 10.1088/0266-5611/29/10/104008. |
[9] |
D. Colton, Y. J. Leung and S. Meng, Distribution of complex transmission eigenvalues for spherically stratified media, Inverse Problems, 31 (2015), 035006, 19pp.
doi: 10.1088/0266-5611/31/3/035006. |
[10] |
R. Duffin and A. C. Schaeffer, Some properties of functions of exponential type, Bull. Amer. Math. Soc., 44 (1938), 236-240.
doi: 10.1090/S0002-9904-1938-06725-0. |
[11] |
B. Levin, Distribution of Zeros of Entire Functions, American Mathematical Society Translation, Providence, Rhode Island, R.I., 1980. |
[12] |
J. McLaughlin and P. Polyakov, On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues, J. Differential Equations, 107 (1994), 351-382.
doi: 10.1006/jdeq.1994.1017. |
[13] |
H. Pham and P. Stefanov, Weyl asymptotics for the transmission eigenvalues for a constant index of refraction, Inverse Prob. Imaging, 8 (2014), 795-810.
doi: 10.3934/ipi.2014.8.795. |
[14] |
W. Rundell and P. Sacks, Reconstruction techniques for classical inverse Sturm-Liouville problems, Math. Comp., 58 (1992), 161-183.
doi: 10.1090/S0025-5718-1992-1106979-0. |
[15] |
J. Sylvester, Transmission eigenvalues in one dimension, Inverse Problems, 29 (2013), 104009, 11pp.
doi: 10.1088/0266-5611/29/10/104009. |
[16] |
G. Wei and H. Xu, Inverse spectral analysis for the transmission eigenvalue problem, Inverse Problems, 29 (2013), 115012, 24pp.
doi: 10.1088/0266-5611/29/11/115012. |
[17] |
W. Young, Introduction to Nonharmonic Fourier Series, Academic Press, San Diego, 2001. |
show all references
References:
[1] |
T. Aktosun, D. Gintides and V. G. Papanicolaou, The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems, 27 (2011), 115004, 17pp.
doi: 10.1088/0266-5611/27/11/115004. |
[2] |
T. Aktosun and V. G. Papanicolaou, Reconstruction of the wave speed from transmission eigenvalues for spherically symmetric variable-speed wave equation, Inverse Problems, 29 (2013), 055007, 19pp.
doi: 10.1088/0266-5611/29/6/065007. |
[3] |
A. Baker, Transcendental Number Theory, Cambridge University Press, Cambridge, 1975. |
[4] |
F. Cakoni and D. Colton, A Qualitative Approach to Inverse Scattering Theory, Applied Mathematical Sciences Series Volume 188, Sringer, New York 2014.
doi: 10.1007/978-1-4614-8827-9. |
[5] |
F. Cakoni, D. Colton and D. Gintides, The interior transmission eigenvalue problem, SIAM J. Math Anal., 42 (2010), 2912-2921.
doi: 10.1137/100793542. |
[6] |
R. Courant and D. Hilbert, Methods of Mathematical Physics, Volume I, Interscience Publishing, New York, 1953. |
[7] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed., Applied Mathematical Sciences, 93. Springer, New York, 2013.
doi: 10.1007/978-1-4614-4942-3. |
[8] |
D. Colton and Y. J. Leung, Complex Eigenvalues and the inverse spectral problem for transmission eigenvalues, Inverse Problems, 29 (2013), 104008, 6pp.
doi: 10.1088/0266-5611/29/10/104008. |
[9] |
D. Colton, Y. J. Leung and S. Meng, Distribution of complex transmission eigenvalues for spherically stratified media, Inverse Problems, 31 (2015), 035006, 19pp.
doi: 10.1088/0266-5611/31/3/035006. |
[10] |
R. Duffin and A. C. Schaeffer, Some properties of functions of exponential type, Bull. Amer. Math. Soc., 44 (1938), 236-240.
doi: 10.1090/S0002-9904-1938-06725-0. |
[11] |
B. Levin, Distribution of Zeros of Entire Functions, American Mathematical Society Translation, Providence, Rhode Island, R.I., 1980. |
[12] |
J. McLaughlin and P. Polyakov, On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues, J. Differential Equations, 107 (1994), 351-382.
doi: 10.1006/jdeq.1994.1017. |
[13] |
H. Pham and P. Stefanov, Weyl asymptotics for the transmission eigenvalues for a constant index of refraction, Inverse Prob. Imaging, 8 (2014), 795-810.
doi: 10.3934/ipi.2014.8.795. |
[14] |
W. Rundell and P. Sacks, Reconstruction techniques for classical inverse Sturm-Liouville problems, Math. Comp., 58 (1992), 161-183.
doi: 10.1090/S0025-5718-1992-1106979-0. |
[15] |
J. Sylvester, Transmission eigenvalues in one dimension, Inverse Problems, 29 (2013), 104009, 11pp.
doi: 10.1088/0266-5611/29/10/104009. |
[16] |
G. Wei and H. Xu, Inverse spectral analysis for the transmission eigenvalue problem, Inverse Problems, 29 (2013), 115012, 24pp.
doi: 10.1088/0266-5611/29/11/115012. |
[17] |
W. Young, Introduction to Nonharmonic Fourier Series, Academic Press, San Diego, 2001. |
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